Revisiting the spatially inhomogeneous condensates in the (1+1) -dimensional chiral Gross–Neveu model via the bosonic two-point function in the infinite-N limit

Abstract

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1+1) -dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer et al 2008 Phys. Rev. D 78 065043; Boehmer and Thies 2009 Phys. Rev. D 80 125038; Thies 2018 Phys. Rev. D 98 096019; Thies 2022 Phys. Rev. D 105 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.